Sunday, December 6, 2009

OCTAL MULTIPLICATION

We multiply the numbers as they are. However, 2 digit or 3 digit products will still remain in one column. As you can see, when we multiplied 5 by 6, we write a 30 below. Not 0 carry 3. Do the following for 2 times 6 to get 12 and so on.

Next, we add the numbers. 30 + 0 is 30. 12 + 5 is 17. 0 + 2 is 2. Sums are still on individual columns.

Here's the tricky part. Since we're dealing with the octal number system ( 8 ), we have to find multiples of 8 closest to each digit. These are 0, 8, 16, 24, 32, 40, 48 and so on...For 30, the closest would be 3 x 8 = 24. So subtract 30 by 24 to get 6. Carry the 3 over to the second digit.

The number we carry over is determined by the number of 8's we had to subtract from 30 to get a difference of less than 8. I.E 30 - 8 = 22 - 8 = 14 - 8 = 6. We subtracted 30 by 8 three times so we add 3 to the digit before. Or it is simply the number we multiply by 8 to get the number closest to 30.

17 + 3 is 20. The multiple ( of 8 ) closest to 20 is 16. So we subtract 20 by 16 to get 4 and carry over a 2 to the 3rd digit.

2 + 2 is 4 . Since this is less than 8, this would be the final answer.